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Carry-over balanced designs for 8 treatments

Those are Williams designs you might say, but it has become clear to me that Williams designs are just a subset of all carry-over balanced designs. Not through hard work of mine, comments by Apn on my previous post Creating Williams designs with even number of products lead to this. Among other things, Apn claimed there were designs which did not confirm to the well known symmetry that each row is the reflection of another row. Related to that was a claim that there is a nine treatment square carry-over balanced design. I made my algorithm faster and in this post I can confirm the former, but the latter is too long a calculation for the algorithm I used.

Code

Code is below. Running the JIT saves half of the time. It is basically a simplified version of my old algorithm, but with a lot of small modifications, basically avoiding loops, ifs and a load of trial and error for speed.